The feasibility problem in (REF ) is reformulated as a rank-minimization problem where, first, the objective is augmented with \(\ell _{2,0}\)  constraints and, then, tractable surrogates of the (non-convex) rank and the \(\ell _{2,0}\)  norm are used. Specifically, consider replacing the rank with the nuclear norm, and the \(\ell _{2,0}\)  norm with the \(\ell _{2,1}\)  norm [1]}, [2]}. The resultant optimization is
\(\lbrace \mathbf {Z}_\text{i}^{(*)}\rbrace _{\text{i}=1}^\text{R}& = \operatornamewithlimits{arg\,min}_{\lbrace \mathbf {Z}_\text{i}\rbrace _{\text{i}=1}^\text{R}} \quad \textstyle \sum _{\text{i}=1}^\text{R}\eta _{\text{i}}\Vert \mathbf {Z}_\text{i}\Vert _* + \sum _{\text{i}=1}^\text{R}\beta _{\text{i}}\Vert \mathbf {Z}_\text{i}\Vert _{2,1} \\& \text{s. to} \quad \mathbf {y}= { \textstyle \sum _{\text{i}=1}^\text{R}\mathbf {M}_\text{i}} \text{vec}\left(\mathbf {Z}_\text{i}\right),\nonumber \) 
